Reworked the 24-cell sketch, much easier to understand now.

Every one of the 12 visible #spinors has a button that brings the yellow spinor (the 1 state) to the clicked one because in 3D spinors double as rotations. (both are #quaternions so there exists a quotient between spinors, which is a rotation).

I think what's clear is that thinking in terms of a spinorial/rotational lattice makes things much easier to grasp than in terms of a vectorial/translational lattice

https://editor.p5js.org/aap/sketches/-N-Bnk_jn

@johncarlosbaez Perhaps you would like to take a look at the sketch again? It should be easier to follow now.

I really have to thank you for bringing my attention to this very beautiful piece of math :)